I am trying to work out a few things as well as a bit of theory-crafting along the way, and seeing what far better players than me think lol.

My playstyle is all bout the burst on the pull etc - PoM and pot before pull, charged up (on pull), RoP (if talented), macro with trinket and arc power - nuke AB til OOM, evocate then conserve phase keeping mana above 70% for equipoise. Is it better to ALWAYS have RoP because to do that would mean a HUGE percentage of damage would have to come from the above scenario being available at points during the fight. IF is much less damage overall but much more movement forgiving.....

I also have 3 very interesting trinkys - 400 ilvl Incandescent Sliver, 385 ilvl Baleful Branch and 380 ilvl First Mate's Spyglass. I'm not 100% sure of which combo to take with passive int's on 2 of em, on use crit or int or a passive permanent crit buff should I be away from others (unless they have it too).

I'm thinking Sliver and Spyglass - purely for the passive intellect and a nice on use crit buff (with other crit procs from 385 ilvl Bloodbough Cowl I've had 60% crit and above with everything going @ once). I was using Branch and Spyglass with the spyglass as my main opening so I got the very high crit as an opener (with most proc's often starting @ same time on pull) and then using the Branch during the 1st equipoise conserve phase. However I'd switch to using the Branch with above macro as not always possible to get same high crit from then on in the fight. Having the Spyglass during conserve phase with equipoise gives tasty numbers.

I am also wondering whether it is a typical arcane mage scenario where my dps is high but overall actual damage is much lower than others. I'm 398 ilvl so I can't compare to toons 410+ for example but I want to compete a bit better, and if possible, improve. Lots of people have told me to switch to frost but sorry to our frosties but I really do not like it - started playing in LK days and frost was ALWAYS pvp - never been able to get used to it as a pve spec!

Definitely might want to analyze your pull cast order. You generally want to use PoM to snag an extra arcane blast within the RoP window at the end.

Is it better to ALWAYS have RoP because to do that would mean a HUGE percentage of damage would have to come from the above scenario being available at points during the fight. IF is much less damage overall but much more movement forgiving.....

It is extremely punishing to miss a RoP phase. If you have to move out, miss a global, get interrupted, target swaps, or the fight length isn't perfect, definitely consider the IF option. RoP *is* the best dps, generally, but you must check your situation. If there is a lot of movement in the fight or the length isn't quite long enough for another RoP you may very well do better with IF.
Perhaps you're a newer arcane mage (or don't raid Mythic and can't be bothered, like me), and you'll play better with IF. You should learn how to use RoP as well though, in case the situation arises where it is obviously better (correct-length short nuke fights, it can be very strong in farm raids).

I also have 3 very interesting trinkys - 400 ilvl Incandescent Sliver, 385 ilvl Baleful Branch and 380 ilvl First Mate's Spyglass. I'm not 100% sure of which combo to take with passive int's on 2 of em, on use crit or int or a passive permanent crit buff should I be away from others (unless they have it too).

You've gotta sim these (SimC addon + RaidBots). Bloodmallet.com is a good resource for getting a general idea, but this will change with your stat setup. If you run RoP, keep in mind the "on use" trinkets can usually be locked into your rune rotation for better damage stacking. Also make sure the fight you are on doesn't require everyone to stack for the Sliver, it immediately kills that trinket.

I am also wondering whether it is a typical arcane mage scenario where my dps is high but overall actual damage is much lower than others. I'm 398 ilvl so I can't compare to toons 410+ for example but I want to compete a bit better, and if possible, improve.

This is actually the way it ends up working out. When we are in burn phase, we do high dps, but evocation alone is a solid 3+ seconds of zero damage, and the conserve phase also drops the overall damage. On a meter, usually we have higher dps but lower overall as you describe. Definitely check out warcraftlogs and compare yourself to the better arcane mages of your level to find out where you can improve.

Your friends are also correct: frost is probably the best spec right now. But I'm too stubborn so I, too, play arcane. It's a lot of work for little gain, so far, but I love it.